CE 3305 Engineering Fluid Mechanics
Spring 2024 Exercise Set 8

LAST NAME, FIRST NAME

R00000000

---

Purpose :

Application of continunity to relate flow area and velocity to volumetric (or mass) flow rate. Application of definition of mean section velocity.

Assessment Criteria :

Completion, plausible solutions, use JupyterLab/Excel or a calculator. Application of problem solving protocol.

---

Problem 1.

A fluid flowing between two plates has a parabolic velocity profile given as $u(y)=\frac{4u_{max}}{h^2}(hy-y^2)$

Determine:

1. Average velocity in terms of $u_{max}$
2. Volumetric discharge for plates of width $w$ (dimension into the sketch)

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

---

Problem 2

Rain falls vertically onto the roof of a building with an average speed of 15 ft/s. The water accumulates in the gutter and flows out the downspout at 12 ft$^3$/min. The building is 18 feet wide.

Determine:

1. Amount of falling rainwater in one cubic foot of air.
2. The number of drops in a cibic foot of air (drop diameter is 0.18 inches; $V_{drop}=\frac{4}{3}\pi r^3$)

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

---

Problem 3

The velocity profile for a fluid in a circular pipe for fully developed turbulent flow is modeled using Prandtl's $\frac{1}{7}$ power law model: $u=U(\frac{y}{R})^{\frac{1}{7}}$

Determine:

1. Average velocity (mean section velocity)
2. Volumetric flow rate

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

---

Problem 4

The pipe system is shown at steady flow with mean section velocities as indicated.

Determine:

1. Outline (draw) a control volume that contains water in the pipe system.
2. Indicate open control surfaces, and show outward pointing area vectors.
3. Indicate flow velocities at these surfaces.

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

---